Quantum Mechanics-I (2018) :: Course given at University of Hyderabad

  Inadequacy of classical theories. Landmarks in rise of quantum theory.
  Review of classical and quantum particle and wave concepts. Uncertainty
  principle. The changes and new concepts brought in by quantum theory.
  Wave mechanics of a single point particle.

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  Optics and mechanics  analogy.
  Time dependent Schrodinger equation. Conservation of probability.
  Interpretation of wave function as probability amplitude. Probability
  current     density. Schrodinger equation for a charged particle. Time
  reversal. Free     particle. Solution of time dependent Schrodinger equation
  for a free particle. Wave packets. Periodic boundary condition and box
  normalization. Free particle in two and three dimensions.
  Eigenfunctions of momentum. Momentum space wave   function. Quantum mechanics
  of a spin half particle.

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Particle in a box. Boundary and   matching conditions on wave function. Energy
  eigenvalues and eigenfunctions. Harmonic oscillator energy eigenvalues and
  eigenfunctions. Periodic potential
  Reflection and transmission through a potential well. Barrier tunnelling.
  General properties of motion in one dimension. 

  Conservation of angular   momentum. Reduction of two body central force
  problem   to one body with   reduced mass. Separation of variables in
  spherical polar coordinates.
  Solution of radial equation for free particle and piece  wise constant
  potentials. Hydrogen atom energy levels  and wave functions. Accidental
  degeneracy of Coulomb energy levels.

  The structure of physical theories.
  Thought experiments and superposition principle in quantum mechanics. States
  and dynamical variables in quantum description of a physical system.
  Probability and average value. Canonical quantization. General form of
  uncertainty  principle. Time evolution. Schrodinger, Heisenberg, and Dirac
  Pictures in quantum mechanics. Density matrix. Identical  particles

  Compatible variables. Commuting observables. Complete
  commuting set. Functions of operators and matrices. Simultaneous eigenvectors
  as basis in Hilbert space. State vectors as set of probability amplitudes.
  Coordinate and momentum representations as examples. Spin matrices and their
  properties. Wave function of a particle with spin.

  Harmonic oscillator energy levels. Angular momentum eigenvalues and
  eigenfunctions. Addition of angular momenta

Time independent first order perturbation theory non degenerate
and degenerate levels. Second order corrections for non degenerate levels.
Rayleigh Ritz Variation method. WKB apprximation.

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